We prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow, derived in Granero-Belinchon and Scrobogna (2019), is well posed in (H)over dot(3/2) (S-1), and globally well-posed if the initial datum is small in (H)over dot(3/2) (S-1).
Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space
Scrobogna S
2021-01-01
Abstract
We prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow, derived in Granero-Belinchon and Scrobogna (2019), is well posed in (H)over dot(3/2) (S-1), and globally well-posed if the initial datum is small in (H)over dot(3/2) (S-1).File in questo prodotto:
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